Energy shaping based methodology was a millstone along robot manipulator control designs [1]} and has been a basic building block for nonlinear control theory [2]}, [3]}. The main idea is to shape the potential energy of the underlined system by a proportional term in the controller such that the closed-loop system has a unique and isolated minimum at the origin where the tracking error is zero. The required damping to achieve the asymptotic stability is injected by a derivative action. The damping injection is also possible when only position is available for feedback through damping propagation. A key to this methodology is to find an appropriate potential and kinetic energy for the closed-loop system. After that, a PD-like controller can be readily obtained by computing the gradient of the potential and the kinetic energy.
